Republican gubernatorial hopeful Rob Astorino will urge President Obama to “put up or shut up’’ on the federal government’s claim that Westchester engages in racial discrimination when Obama visits the new Tappan Zee Bridge project on Wednesday, The Post has learned.

On Monday, Astorino, the Westchester County executive, plans to extend the invitation to Obama and Gov. Cuomo to take some time during his scheduled tour of the $4 billion bridge project to visit Westchester communities “in search of any evidence of racial discrimination.”

“The president and the governor can start in the town of New Castle,’’ said Astorino campaign spokesman William O’Reilly, referring to the small, wealthy and largely rural community where Cuomo lives in a home owned by his significant other, celebrity chef Sandra Lee.

“The county executive plans to tell the president, ‘Your agency has been torturing Westchester County for five years, trying to make a national example out of it. If you think there’s discrimination here, show it to us, find a village or a town or a city where the zoning is discriminating, and we’ll dissolve it. We can point to eight studies that have been done saying that’s not the case, that the only barriers to home ownership in Westchester are economic, not racial or ethnic,’ ’’ O’Reilly said.

The federal Department of Housing and Urban Development, once headed by Cuomo, has repeatedly charged that Astorino is failing to abide by a 5-year-old agreement requiring Westchester towns — including New Castle — to change allegedly racially discriminatory zoning laws in order to encourage the building of “affordable housing’’ for lower-income residents. It is also holding back $10 million in federal aid as punishment.

The emotionally charged dispute was widely aired by Astorino’s Democratic opponent in last fall’s election but, despite a 2-1 Democrat enrollment advantage, Astorino won re-election in a landslide.

The Cuomo-controlled Democratic Party has begun attacking Astorino in TV ads over HUD’s charges, although the governor himself has repeatedly refused to say if he agrees with his old agency’s allegations.

Obama’s tour will take place as the state GOP holds its nominating convention in Westchester to officially declare Astorino its standard-bearer against Cuomo.

Important state Republicans are warning that Senate GOP Leader Dean Skelos is, as one told The Post, about to “sell out’’ Astorino and GOP principles by supporting an expansive measure for the public funding of elections.

The move would enable Cuomo to win the endorsement of the leftist Working Families Party (WFP), whose support could be crucial for the governor in a tight election.

“Once again, the Senate Republicans are only focused on the next election,’’ said a GOP insider who has close ties to Astorino.

Cuomo, who Democrats say is desperately trying to ensure a large electoral victory over Astorino, is out of favor with many in the WFP because of his opposition to Mayor de Blasio’s proposed tax on the wealthy and the governor’s cozy relationship with Senate Republicans, who have attacked public-funding systems like the one in New York City as corruption-inducing wastes of tax money.

Skelos reversed course in late March and agreed to a one-year public-financing scheme for this year’s state comptroller’s race as a tactic to help Cuomo blunt criticism from influential public-financing proponents, including major labor unions and the son of left-wing billionaire George Soros.

That plan blew up in Cuomo’s face when several “good government’’ groups denounced it as worthless and Democratic state Comptroller Tom DiNapoli announced he would not participate.

Insiders say Skelos, who badly split the state GOP last year by backing Cuomo’s anti-gun ownership “Safe Act,’’ is willing to back a broader public-financing plan in exchange for Cuomo’s commitment not to campaign against Senate Republicans this year.

Assembly Speaker Sheldon Silver, in his leadership position since 1994, is described by lobbyists as the “Cheshire Cat of the Capitol’’ now that Cuomo has been tarnished by a scandal over his firing of the anti-corruption Moreland Act commission, and allegations he meddled with it.

Silver, often cited by critics in past years as Exhibit A of much of what’s wrong at the Capitol, was described by one prominent lobbyist as “smiling away as Cuomo, Mr. Integrity himself, has been badly damaged by his own scandal.”